1. Field of the Invention
This invention relates to quantum computing and to solid state devices that use superconducting materials to create and maintain coherent quantum states such as required for quantum computing.
2. Description of Related Art
Research on what is now called quantum computing traces back to Richard Feynman, [R. Feynman, Int. J. Theor. Phys., 21, 467-488 (1982)]. Feynman noted that quantum systems are inherently difficult to simulate with conventional computers but that observing the evolution of a quantum system could provide a much faster way to solve the same computational problems. In particular, solving a theory for the behavior of a quantum system commonly involves solving a differential equation related to the Hamiltonian of the quantum system. Observing the behavior of the quantum system provides information regarding the solutions to the equation.
Further efforts in quantum computing were initially concentrated on xe2x80x9csoftware developmentxe2x80x9d or building of the formal theory of quantum computing. Software for quantum computing attempts to set the Hamiltonian of a quantum system to correspond to a problem requiring solution. Milestones in these efforts were the discoveries of the Shor and Grover algorithms. [See P. Shor, SIAM J. of Comput., 26:5, 1484-1509 (1997); L. Grover, Proc. 28th STOC, 212-219 (1996); and A. Kitaev, LANL preprint quant-ph/9511026 (1995)]. In particular, the Shor algorithm permits a quantum computer to factorize natural numbers. The showing that fault-tolerant quantum computation is theoretically possible opened the way for attempts at practical realizations of quantum computers. [See E. Knill, R. Laflamme, and W. Zurek, Science, 279, p. 342 (1998).]
One proposed application of a quantum computer is factoring of large numbers. In such an application, a quantum computer could render obsolete all existing encryption schemes that use the xe2x80x9cpublic keyxe2x80x9d method. In another application, quantum computers (or even a smaller scale device, a quantum repeater) could allow absolutely safe communication channels, where a message, in principle, cannot be intercepted without being destroyed in the process. [See H. J. Briegel et al., LANL preprint quant-ph/9803056 (1998) and the references therein.]
Quantum computing generally involves initializing the states of N qubits (quantum bits), creating controlled entanglements among the N qubits, allowing the quantum states of the qubits to evolve under the influence of the entanglements, and reading the qubits after they have evolved. A qubit is conventionally a system having two degenerate quantum states, and the initial state of the qubit typically has non-zero probabilities of being found in either degenerate state. Thus, N qubits define an initial state that is a combination of 2N degenerate states. The entanglements control the evolution of the distinguishable quantum states and define calculations that the evolution of the quantum states perform. This evolution, in effect, performs 2N simultaneous calculations. Reading the qubits after evolution is complete determines the states of the qubits and the results of the calculations.
Several physical systems have been proposed for the qubits in a quantum computer. One system uses chemicals having degenerate spin states. Nuclear magnetic resonance (NMR) techniques can read the spin states. These systems have successfully implemented the Shor algorithm for factoring of a natural number (15). However, efforts to expand such systems up to a commercially useful number of qubits face difficult challenges.
Another physical system for implementing a qubit includes a superconducting reservoir, a superconducting island, and a dirty Josephson junction that can transmit a Cooper pair (of electrons) from the reservoir into the island. The island has two degenerate states. One state is electrically neutral, but the other state has an extra Cooper pair on the island. A problem with this system is that the charge of the island in the state having the extra Cooper pair causes long range electric interactions that interfere with the coherence of the state of the qubit. The electric interactions can force the island into a state that definitely has or lacks an extra Cooper pair. Accordingly, the electric interactions can end the evolution of the state before calculations are complete or qubits are read. This phenomenon is commonly referred to as collapsing the wavefunction, loss of coherence, or decoherence.
Research is continuing and seeking a structure that implements a quantum computer having a sufficient number of qubits to perform useful calculations.
In accordance with the invention, a qubit includes a superconducting island that a Josephson junction separates from a superconducting bank. The island has a crystal orientation that differs from the crystal orientation of the reservoir, and a grain boundary between the island and reservoir forms a clean (ballistic) Josephson junction. One or both of the island and the bank are D-wave superconductors so that a ground state current flows at the Josephson junction. The ground state of the supercurrent at the Josephson junction is twice degenerate with the magnetic moment produced by the supercurrent distinguishing the two states. The crystal orientation of the island relative to the bank controls the equilibrium phase difference in the order parameter across the junction and therefore the tunneling probabilities between the ground states.
To read the supercurrent state associated with the island, a single electron transistor (SET) or parity key can connect the island to ground. When the SET is biased to conduct, the current through the SET collapses supercurrent state to a state with fixed magnetic moment and fixes the supercurrent in that state. Thus, upon completion of a calculation, a control circuit biases the SET to conduct, and the magnetic moment at the Josephson junction is fixed in a particular state and can be dependably read.
To form a quantum register, multiple Josephson junctions can couple respective superconducting islands to a superconducting bank, and a current through the bank can initialize the quantum states of the supercurrents at the junctions. Single electron transistors (SETs) or parity keys interconnect the islands to create controlled entanglements as required for quantum computing. After completion of the computing, other SETs or parity keys connect the islands to ground and freeze the supercurrents at the Josephson junctions into states having definite magnetic moments. This freezing maintains the states for subsequent read operations that measure the local magnetic moments or magnetic flux.
One embodiment of the invention is a quantum computing structure such as a quantum coherer or a quantum register that includes a bank of a superconducting material and an island of a superconducting material, wherein at least one of the island and the bank is a d-wave superconductor. The normal-conductor portion of a clean Josephson junction can be, for example, a grain boundary between the bank and the island. Optionally, a single electron transistor (SET) or a parity key is between the island and ground. The orientation of the supercurrent through the junction is fixed when the SET is conductive and can evolve when the SET is non-conductive. As another option, the structure also includes a second bank of superconducting material, and a Josephson junction between the first and second banks. Operation of a SET between the second bank and the island selectively initializes the supercurrent""s quantum state according to the phase of the order parameter in the first or second bank.
Another embodiment of the invention is a quantum register that includes: a bank of a superconducting material; a plurality of islands of superconducting material; and a plurality of clean Josephson junctions. Each clean Josephson junction is between the bank and a corresponding one of the islands. One or both of the island and the bank include a d-wave superconductor. The quantum register optionally includes three sets of SETs. Each SET in a first set is between ground and a corresponding one of the islands. Each SET in the second set is between a corresponding pair of the islands. Each SET in the third set is between a second bank and a corresponding one of the islands. The Josephson junction creates an order parameter phase difference between the first and second banks. The second bank and the third set of SETs can be used for selective initialization of supercurrents at the junctions according to the phase of the second bank.
In accordance with another embodiment of the invention, a quantum computing method cools a structure including a bank and an island to a temperature that makes the bank and the island superconducting and suppresses the decoherence processes in the system. The structure includes a junction that is a clean Josephson junction between the island and the bank. After the structure is at the appropriate temperature, the method establishes a supercurrent at the junction in a quantum state that is an admixture of a first state having a first magnetic moment and a second state having a second magnetic moment. The supercurrent at the junction is a ground state current arising from use of a d-wave superconductor in the structure and can be set by running a current through the bank. The quantum state evolves according to probabilities for tunneling between the first and second ground states. The evolution performs the quantum computing. Determining a measured magnetic moment or flux due to the supercurrent at the junction determines a result from the quantum computing.
In accordance with another aspect of the invention, determining the measured magnetic moment includes: grounding the island to fix the supercurrent in the first or second state; and measuring the magnetic flux produced by the supercurrent while the island is grounded.
Typically, the quantum register further includes a plurality of islands and a plurality of junctions, each junction being a clean Josephson junction between the bank and a corresponding island. The quantum states of the supercurrents at the junctions evolve according to the conductivities of transistors that couple islands together. These transistors create entanglements of the quantum states of the islands. The manufacturer of the quantum register can select for each island, a crystal orientation according to the initial quantum state desired for the island.